Derivative-Enhanced Rational Polynomial Chaos for Uncertainty Quantification

Recently, Polynomial Chaos (PC) has been proposed as efficient approach for performing uncertainty quantification in the the context of electronic design automation. A related approach, Rational Polynomial Chaos (RPC) was later developed for applications that exhibit a large variation in the quantity of interest. One of the key bottlenecks for both PC and RPC is the number of circuit evaluation needed, particularly as the number of random parameters increases (often referred to as the curse of dimentionality). In this paper, we propose an approach that uses sensitivity information to significantly reduce the number of circuit evaluations needed for Rational Polynomial Chaos. Numerical examples are given to illustrate the accuracy and efficiency of the proposed approach.